Question: Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}6x+3y &= 4 \\ 2x+6y &= -7\end{align*}$
Answer: Begin by moving the $y$ -term in the second equation to the right side of the equation. $2x = -6y-7$ Divide both sides by $2$ to isolate $x$ $x = {-3y - \dfrac{7}{2}}$ Substitute this expression for $x$ in the first equation. $6({-3y - \dfrac{7}{2}}) + 3y = 4$ $-18y - 21 + 3y = 4$ Simplify by combining terms, then solve for $y$ $-15y - 21 = 4$ $-15y = 25$ $y = -\dfrac{5}{3}$ Substitute $-\dfrac{5}{3}$ for $y$ in the top equation. $6x+3( -\dfrac{5}{3}) = 4$ $6x-5 = 4$ $6x = 9$ $x = \dfrac{3}{2}$ The solution is $\enspace x = \dfrac{3}{2}, \enspace y = -\dfrac{5}{3}$.